Vaccine supply chain optimization can benefit from hierarchical time series
forecasting, when grouping the vaccines by type or location. However, forecasts
of different hierarchy levels become incoherent when higher levels do not match
the sum of the lower levels forecasts, which can be addressed by reconciliation
methods.
In this paper, we tackle the vaccine sale forecasting problem by modeling
sales data from GSK between 2010 and 2021 as a hierarchical time series. After
forecasting future values with several ARIMA models, we systematically compare
the performance of various reconciliation methods, using statistical tests. We
also compare the performance of the forecast before and after COVID. The
results highlight Minimum Trace and Weighted Least Squares with Structural
scaling as the best performing methods, which provided a coherent forecast
while reducing the forecast error of the baseline ARIMA.

本文通过对 2010 年至 2021 年葛兰素史克疫苗销售数据进行建模，使用多种 ARIMA 模型预测未来数值，并运用统计检验系统地比较各种调和方法的表现，比较 COVID 前后预测的表现。结果表明，最小迹线和加权最小二乘法与结构缩放是最佳表现的方法，提供了连贯的预测，同时减少了基准 ARIMA 的预测误差。

疫苗供应链优化的预测协调

Forecast reconciliation for vaccine supply chain optimization

A stock market is considered as one of the highly complex systems, which
consists of many components whose prices move up and down without having a
clear pattern. The complex nature of a stock market challenges us on making a
reliable prediction of its future movements. In this paper, we aim at building
a new method to forecast the future movements of Standard & Poor's 500 Index
(S&P 500) by constructing time-series complex networks of S&P 500 underlying
companies by connecting them with links whose weights are given by the mutual
information of 60-minute price movements of the pairs of the companies with the
consecutive 5,340 minutes price records. We showed that the changes in the
strength distributions of the networks provide an important information on the
network's future movements. We built several metrics using the strength
distributions and network measurements such as centrality, and we combined the
best two predictors by performing a linear combination. We found that the
combined predictor and the changes in S&P 500 show a quadratic relationship,
and it allows us to predict the amplitude of the one step future change in S&P
500. The result showed significant fluctuations in S&P 500 Index when the
combined predictor was high. In terms of making the actual index predictions,
we built ARIMA models. We found that adding the network measurements into the
ARIMA models improves the model accuracy. These findings are useful for
financial market policy makers as an indicator based on which they can
interfere with the markets before the markets make a drastic change, and for
quantitative investors to improve their forecasting models.

本文提出了一种基于时间序列复杂网络（complex networks）和互信息（mutual information）的新方法来预测标准普尔 500 指数（S&P 500）未来的变化，并且使用这种方法可以明显提高建立 ARIMA 模型的准确性，这些发现可以为金融市场决策者提供指示，在市场发生剧烈变化之前干预市场。同时，对于量化投资者来说，这也可以提高他们的预测模型。